In a given training week, a swimmer completes:
- 1/4 mile on day one
- 2/5 mile on day two
- 3/7 mile on day three
How many total miles does the athlete swim in the given week?
Answer (3)
We'll have to add up all the fractions. First, find the LCM of the denominators. To do this, we'll use the listing method.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, all the way to 140. 5: 5, 10, 15, 20, 25, 30, 35, all the way to 140. 7: 7, 14, 21, 28, 35, 42, 49, all the way to 140.
So, 140 is the Least Common Multiple.
Multiply the numerator of 1 as many times you multiplied 4 to get to 140, which is 35. 1 x 35 = 35.
Multiply the numerator of 2 as many times you multiplied 5 to get to 140, which is 28. 2 x 28 = 56
Multiply the numerator of 3 as many times you multiplied 7 to get to 140, which is 20. 3 x 20 = 60.
So: 35/140 + 56/140 + 60/140 =35/140 + 116/140 =151/140 =1 11/140
So, the swimmer swam 1 and 11/140th of a mile.
**We’ll have to add up all the fractions. **
**First, find the LCM of the denominators. **
**To do this, we’ll use the listing method. **
**
**
**4: 4, 8, 12, 16, 20, 24, 28, 32, 36, all the way to 140. **
**5: 5, 10, 15, 20, 25, 30, 35, all the way to 140. **
**7: 7, 14, 21, 28, 35, 42, 49, all the way to 140. **
**
**
**So, 140 is the Least Common Multiple. **
**
**
**Multiply the numerator of 1 as many times you multiplied 4 to get to 140, which is 35. **
**1 x 35 = 35. **
**
**
**Multiply the numerator of 2 as many times you multiplied 5 to get to 140, which is 28. **
**2 x 28 = 56 **
**
**
**Multiply the numerator of 3 as many times you multiplied 7 to get to 140, which is 20. **
**3 x 20 = 60. **
**
**
**So: 35/140 + 56/140 + 60/140 **
**=35/140 + 116/140 **
**=151/140 **
**=1 11/140 **
**
**
So, the swimmer swam 1 and 11/140th of a mile. ;
The total distance swum by the swimmer in a week is 1 and 140 11 miles. This was calculated by finding a common denominator for the three fractions of distances completed each day. By converting and adding the fractions, the final total was obtained.
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